A unit matrix is a square matrix with 1s on the main diagonal and 0s elsewhere. It is also known as an identity matrix since it has a unique property to leave any matrix unchanged under matrix multiplication. The unit matrix is a fundamental concept in linear algebra and often used in various fields of mathematics and engineering. Synonyms for the unit matrix include identity matrix, unity matrix, multiplication identity, and Kronecker delta. However, regardless of the name, the unit matrix's primary purpose is to associate an element with the same element, just like how the number 1 is associated with itself in basic arithmetic.